A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

Try this matching game which will help you recognise different ways of saying the same time interval.

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Can you find the chosen number from the grid using the clues?

In this matching game, you have to decide how long different events take.

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

What two-digit numbers can you make with these two dice? What can't you make?

Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

What happens when you try and fit the triomino pieces into these two grids?

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

Find out what a "fault-free" rectangle is and try to make some of your own.

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

Have a go at this game which has been inspired by the Big Internet Math-Off 2019. Can you gain more columns of lily pads than your opponent?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Can you find all the different ways of lining up these Cuisenaire rods?

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

How many trains can you make which are the same length as Matt's, using rods that are identical?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

Investigate the different ways you could split up these rooms so that you have double the number.

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?